This was *always* the distinction, and anyone telling you otherwise *was not there*. "Web 2.0" as a phrase came about in the 2003 - 2007 era, when people were talking about "mashups" a ton (like taking data from your internal database and using it on a Google Map component to show your store locations).
The era of "static HTML web pages" lasted like... a minute. Web servers were doing CGI within a year or two of HTML hitting the scene. In 1996 when I started to write Web pages, it was already not uncommon to use Perl, bash script, etc. to put a page together, using the URL or POST parameters to make decisions (seriously, anyone who says Web 1 was static only forgets that POST, PUT, etc. were there on Day 1!).
Stuff like this reminds me that a proper "History of CS" class should be mandatory for a CS degree.
J.Ja